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Feb
6
comment independent variables or not
@DilipSarwate: I think they are Normal and independent in fact. Although I am not sure why the sum and difference are independent in that case. If $X$ and $Y$ are normal and indpnt, then $X+Y$ is also normal, so as $X-Y$, why the last two are independent then?
Feb
6
accepted Is $X_t$ a martingale?
Feb
6
comment independent variables or not
@DilipSarwate: from aboove I see the statement is in fact incorrect, would that make a difference if $X$ and $Y$ are iid?
Feb
6
asked independent variables or not
Feb
6
comment Is $X_t$ a martingale?
I see, thanks. I would guess because they both involve the information at time $u$, so they overlap there and not independent? Then, second part ends up being $\int_u^t E[W_s/F_u]ds=W_u(t-u)$? And clearly this is not zero and therefore it is not a martingale?
Feb
6
revised Is $X_t$ a martingale?
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Feb
6
revised Is $X_t$ a martingale?
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Feb
6
asked Is $X_t$ a martingale?
Oct
31
awarded  Popular Question
Sep
11
awarded  Popular Question
Jul
2
awarded  Curious
Apr
17
asked difference of the values of a function is an integral
Oct
28
awarded  Nice Question
Apr
21
asked relation between Holder continuous and weakly differentiable for the coefficients of a pde
Apr
17
revised matrix with distinct bounded eigen values is bounded?
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Apr
16
revised matrix with distinct bounded eigen values is bounded?
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Apr
15
asked matrix with distinct bounded eigen values is bounded?
Mar
22
revised Existence of the degenerate elliptic PDE coefficient condition
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Mar
11
comment Existence of the degenerate elliptic PDE coefficient condition
ok, but the condition saying $c \leq c_0 <0$ doesn't make sense to me. First, consider a backward pde $v_t+v_{xx}=0$, which doesn't satisfy that condition. But having a change of variables as $u:=e^{ct}v,c<0$ I have an equation for $u$: $u_t+u_{xx}-cu=0$ which satisfies the condition and then there is existence. But the two equations are equivalent up to a change of variables so they both either have it or not. Another argument, we trivially know that heat equation, can be viewed as a degenerate elliptic equation and has a solution but does't not satisfy the property of having $c\leq c_0<0$.
Mar
11
comment Existence of the degenerate elliptic PDE coefficient condition
So, coefficient $c$ affects coercivity? Isn't it a property of the coefficint in front of the second order operator? I have looked at your answer, I don't think it is related to my question as I rather have issues with understanding of the existence of the solutions to the basic elliptic and parabolic equations, just don't have any other book on parabolic equations at hands right now.